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The occurrence of giant edge localized modes (ELMs) in DIII-D has previously been correlated with the violation of the ballooning stability criterion at the plasma edge. These results are extended in the paper. It is demonstrated theoretically that flux surfaces near the separatrix of properly elongated and triangulated plasmas may be moved into the connection region between the first and second stability regions for ideal MHD ballooning modes, when q is high and the shear is low near the plasma surface. The edge flux surfaces are then predicted to have no limit to the sustainable pressure gradient. Experimentally, giant ELMs disappear in these highly shaped plasmas. However, the edge pressure gradient does not increase and 'grassy' ELM behaviour appears instead. These results lend further support to the hypothesis that giant ELMs in DIII-D are triggered by ideal ballooning mode instabilities, but they indicate that giant ELM and grassy ELM behaviour may arise from somewhat different mechanisms.

Low-{ital q} ({ital q}{sub 95}{lt}3) double-null divertor discharges with values of the volume-average toroidal beta as high as 9.3% have been operated in the DIII-D tokamak (Fusion Technol. {bold 8}, 441 (1985)). In discharges with {ital q}{sub 95}{approx}5, values of {beta}{sub {ital T}}/({ital I}/{ital aB}) as high as 5 have been obtained. These discharges are shown to be at or below the stability limit to the value of beta for infinite-{ital n}, ideal ballooning modes. The discharges are significantly below the beta limit for ideal,low toroidal mode number kink modes. The kink mode beta limit is shown to be strongly dependent on the radial profiles of plasma pressure and current. The theoretical beta limit in DIII-D is shown to be in the range {beta}{sub {ital T}}/({ital I}/{ital aB})=4 --5 depending on the value of {ital I}/{ital aB}, and this is consistent with the experiment. High-beta discharges have been operated with ion temperature up to 17 keV. Steady-state, high-beta, low-{ital q} operation is demonstrated by a discharge with {ital I}/{ital aB}=2.6, {ital q}{sub 95}=2.7, in which {beta}{sub {ital T}}{gt}7% is maintained for 1.5 sec.

A study of plasma equilibrium and stability in a tokamak with an unsaturated iron cpre is presented. A spool model is developed for the iron core. Both a simplified force balance code and a Grad-Shafranov solver are used to study the plasma equilibrium. It is observed that the iron can strongly modify the conditions for equilibrium and stability, and in some cases an infinite cylinder model for the iron core is not adequate. Corrected criteria for plasma position stability in the presence of an iron core are introduced.

I. Introduction (Z. Lin, G. Y. Fu, J. Q. Dong) II. Role of theory and simulation in fusion sciences 1. The Impact of theory and simulation on tokomak experiments (H. R. Wilson, T.S. Hahm and F. Zonca) 2. Tokomak Transport Physics for the Era of ITER: Issues for Simulations (P.H. Diamond and T.S. Hahm) III. Status of fusion simulation and modeling 1. Nonlinear Governing Equations for Plasma Simulations (T. S. Hahm) 2. Equilibrium and stability (L.L. Lao, J. Manickam) 3. Transport modeling (R.E. Waltz) 4. Nonlinear MHD (G.Y. Fu) 5. Turbulence (Z. Lin and R.E. Waltz) 6. RF heating and current drive (D.A. Batchelor) 7. Edge physics Simulations (X.Q. Xu and C.S. Chang) 8. Energetic particle physics (F. Zonca, G.Y. Fu and S.J. Wang) 9. Time-dependent Integrated Modeling (R.V. Budny) 10. Validation and verification (J. Manickam) IV. Major initiatives on fusion simulation 1. US Scientific Discovery through Advanced Computing (SciDAC) Program & Fusion Energy Science (W. Tang) 2. EU Integrated Tokamak Modelling (ITM) Task Force (A. Becoulet) 3. Fusion Simulations Activities in Japan (A. Fukuyama, N. Nakajima, Y. Kishimoto, T. Ozeki, and M. Yagi) V. Cross-disciplinary research in fusion simulation 1. Applied mathematics: Models, Discretizations, and Solvers (D.E. Keyes) 2. Computational Science (K. Li) 3. Scientific Data and Workflow Management (S. Klasky, M. Beck, B. Ludaescher, N. Podhorszki, M.A. Vouk) 4. Collaborative tools (J. Manickam)

One modeling framework for integrated tasks (OMFIT) is a comprehensive integrated modeling framework which has been developed to enable physics codes to interact in complicated workflows, and support scientists at all stages of the modeling cycle. The OMFIT development follows a unique bottom-up approach, where the framework design and capabilities organically evolve to support progressive integration of the components that are required to accomplish physics goals of increasing complexity. OMFIT provides a workflow for easily generating full kinetic equilibrium reconstructions that are constrained by magnetic and motional Stark effect measurements, and kinetic profile information that includes fast-ion pressure modeled by a transport code. It was found that magnetic measurements can be used to quantify the amount of anomalous fast-ion diffusion that is present in DIII-D discharges, and provide an estimate that is consistent with what would be needed for transport simulations to match the measured neutron rates. OMFIT was used to streamline edge-stability analyses, and evaluate the effect of resonant magnetic perturbation (RMP) on the pedestal stability, which have been found to be consistent with the experimental observations. The development of a five-dimensional numerical fluid model for estimating the effects of the interaction between magnetohydrodynamic (MHD) and microturbulence, and its systematic verification against analytic models was also supported by the framework. OMFIT was used for optimizing an innovative high-harmonic fast wave system proposed for DIII-D. For a parallel refractive index , the conditions for strong electron-Landau damping were found to be independent of launched and poloidal angle. OMFIT has been the platform of choice for developing a neural-network based approach to efficiently perform a non-linear multivariate regression of local transport fluxes as a function of local dimensionless parameters. Transport predictions for thousands of DIII-D discharges showed excellent agreement with the power balance calculations across the whole plasma radius and over a broad range of operating regimes. Concerning predictive transport simulations, the framework made possible the design and automation of a workflow that enables self-consistent predictions of kinetic profiles and the plasma equilibrium. It is found that the feedback between the transport fluxes and plasma equilibrium can significantly affect the kinetic profiles predictions. Such a rich set of results provide tangible evidence of how bottom-up approaches can potentially provide a fast track to integrated modeling solutions that are functional, cost-effective, and in sync with the research effort of the community.

Magnetic measurements together with kinetic profile and motional Stark effect measurements are used in full kinetic equilibrium reconstructions to test the Sauter and NEO bootstrap current models in a DIII-D high- EAST-demonstration experiment. This aims at developing on DIII-D a high bootstrap current scenario to be extended on EAST for a demonstration of true steady-state at high performance and uses EAST-similar operational conditions: plasma shape, plasma current, toroidal magnetic field, total heating power and current ramp-up rate. It is found that the large edge bootstrap current in these high- plasmas allows the use of magnetic measurements to clearly distinguish the two bootstrap current models. In these high collisionality and high- plasmas, the Sauter model overpredicts the peak of the edge current density by about 30%, while the first-principle kinetic NEO model is in close agreement with the edge current density of the reconstructed equilibrium. These results are consistent with recent work showing that the Sauter model largely overestimates the edge bootstrap current at high collisionality (Belli et al 2014 Plasma Phys. Control. Fusion 56 045006).

The ICRF heating in toroidal plasmas is studied using two global simulation codes: a full wave field solver TASK/WM and a drift kinetic equation solver GNET. The codes are applied to both tokamaks and helical systems. The full wave code TASK/WM evaluates the realistic wave electric field, in which the effect of the self‐consistent non‐Maxwellian velocity distribution on the wave propagation is taken into account. GNET solves a linearized drift kinetic equation (5D phase‐space) for energetic ions including complicated behavior of trapped particles in helical systemsCharacteristics of energetic ion distributions in the phase space are investigatedSelf‐consistent analysis including the effect of energetic ion distribution on the fast wave propagation is also reported for tokamak plasmas.

This work investigates the potential roles played by the scrape-off-layer current (SOLC) in MHD activity of tokamak plasmas, including effects on stability. SOLCs are found during MHD activity that are: (1) slowly growing after a mode-locking-like event, (2) oscillating in the several kHz range and phase-locked with magnetic and electron temperature oscillations, (3) rapidly growing with a sub-ms time scale during a thermal collapse and a current quench, and (4) spiky in temporal behavior and correlated with spiky features in Da signals commonly identified with the edge localized mode (ELM). These SOLCs are found to be an integral part of the MHD activity, with a propensity to flow in a toroidally non-axisymmetric pattern and with magnitude potentially large enough to play a role in the MHD stability. Candidate mechanisms that can drive these SOLCs are identified: (a) toroidally non-axisymmetric thermoelectric potential, (b) electromotive force (EMF) from MHD activity, and (c) flux swing, both toroidal and poloidal, of the plasma column. An effect is found, stemming from the shear in the field line pitch angle, that mitigates the efficacy of a toroidally non-axisymmetric SOLC to generate a toroidally non-axisymmetric error field. Other potential magnetic consequences of the SOLC are identified: (i) its error field can introduce complications in feedback control schemes for stabilizing MHD activity and (ii) its toroidally non-axisymmetric field can be falsely identified as an axisymmetric field by the tokamak control logic and in equilibrium reconstruction. The radial profile of a SOLC observed during a quiescent discharge period is determined, and found to possess polarity reversals as a function of radial distance.

Localized currents driven by pressure gradients play a pivotal role in the magnetohydrodynamic stability of toroidal plasma confinement devices. We have measured the currents generated in the edge of L- (low) and H- (high confinement) mode discharges on the DIII-D tokamak, utilizing the Zeeman effect in an injected lithium beam to obtain high resolution profiles of the poloidal magnetic field. We find current densities in excess of 1 MA/m{sup 2} in a 1 to 2 cm region near the peak of the edge pressure gradient. These values are sufficient to challenge edge stability theories based on specific current formation models.

Research on the Spherical Torus (or Spherical Tokamak) is being pursued to explore the scientific benefits of modifying the field line structure from that in more moderate aspect-ratio devices, such as the conventional tokamak. The Spherical Tours (ST) experiments are being conducted in various U.S. research facilities including the MA-class National Spherical Torus Experiment (NSTX) at Princeton, and three medium-size ST research facilities: Pegasus at University of Wisconsin, HIT-II at University of Washington, and CDX-U at Princeton. In the context of the fusion energy development path being formulated in the U.S., an ST-based Component Test Facility (CTF) and, ultimately a Demo device, are being discussed. For these, it is essential to develop high-performance, steady-state operational scenarios. The relevant scientific issues are energy confinement, MHD stability at high beta (B), noninductive sustainment, ohmic-solenoid-free start-up, and power and particle handling. In the confinement area, the NSTX experiments have shown that the confinement can be up to 50% better than the ITER-98-pby2 H-mode scaling, consistent with the requirements for an ST-based CTF and Demo. In NSTX, CTF-relevant average toroidal beta values bT of up to 35% with the near unity central betaT have been obtained. NSTX will be exploring advanced regimes where bT up to 40% can be sustained through active stabilization of resistive wall modes. To date, the most successful technique for noninductive sustainment in NSTX is the high beta-poloidal regime, where discharges with a high noninductive fraction ({approx}60% bootstrap current + neutral-beam-injected current drive) were sustained over the resistive skin time. Research on radio-frequency-based heating and current drive utilizing HHFW (High Harmonic Fast Wave) and EBW (Electron Bernstein Wave) is also pursued on NSTX, Pegasus, and CDX-U. For noninductive start-up, the Coaxial Helicity Injection (CHI), developed in HIT/HIT-II, has been adopted on NSTX to test the method up to Ip {approx} 500 kA. In parallel, start-up using radio-frequency current drive and only external poloidal field coils are being developed on NSTX. The area of power and particle handling is expected to be challenging because of the higher power density expected in the ST relative to that in conventional aspect-ratio tokamaks. Due to its promise for power and particle handling, liquid lithium is being studied in CDX-U as a potential plasma-facing surface for a fusion reactor.

An interactive IDL based wrapper, IEFIT, has been created for the magnetic equilibrium reconstruction code EFIT written in FORTRAN. It allows high temperature fusion physicists to rapidly optimize a plasma equilibrium reconstruction by eliminating the unnecessarily repeated initialization in the conventional approach along with the immediate display of the fitting results of each input variation. It uses a new IDL based graphics package, GaPlotObj, developed in cooperation with Fanning Software Consulting, that provides a unified interface with great flexibility in presenting and analyzing scientific data. The overall interactivity reduces the process to minutes from the usual hours.

The National Spherical Torus Experiment (NSTX) has produced toroidal plasmas at low aspect ratio (A = R/a = 0.86 m/0.68 m approximately equal to 1.3, where R is the major radius and a is the minor radius of the torus) with plasma currents of 1.4 MA. The rapid development of the machine has led to very exciting physics results during the first full year of physics operation. Pulse lengths in excess of 0.5 sec have been obtained with inductive current drive. Up to 4 MW of High Harmonic Fast Wave (HHFW) heating power has been applied with 6 MW planned. Using only 2 MW of HHFW heating power clear evidence of electron heating is seen with HHFW, as observed by the multi-point Thomson scattering diagnostic. A noninductive current drive concept known as Coaxial Helicity Injection (CHI) has driven 260 kA of toroidal current. Neutral-beam heating power of 5 MW has been injected. Plasmas with beta toroidal (= 2 mu(subscript ''0'') /B(superscript ''2'') = a measure of magnetic confinement efficiency ) of 22% have been achieved, as calculated using the EFIT equilibrium reconstruction code. Beta-limiting phenomena have been observed, and the maximum beta toroidal scales with I(subscript ''p'')/aB(subscript ''t''). High frequency (>MHz) magnetic fluctuations have been observed. High-confinement mode plasmas are observed with confinement times of >100 msec. Beam-heated plasmas show energy confinement times in excess of those predicted by empirical scaling expressions. Ion temperatures in excess of 2.0 keV have been measured, and power balance suggests that the power loss from the ions to the electrons may exceed the calculated classical input power to the ions.

Recent DIII-D experiments using off-axis electron cyclotron current drive (ECCD) have demonstrated the ability to modify the current profile in a plasma with toroidal beta near 3%. The resulting plasma simultaneously sustains the key elements required for Advanced Tokamak operation: high bootstrap current fraction, high beta, and good confinement. More than 85% of the plasma current is driven by noninductive means. ECCD is observed to produce strong negative central magnetic shear, which in turn acts to trigger confinement improvements in all transport channels in the plasma core.

The DIII-D tokamak magnetic diagnostic system [E. J. Strait, Rev. Sci. Instrum. 77, 023502 (2006)] has been upgraded to significantly expand the measurement of the plasma response to intrinsic and applied non-axisymmetric "3D" fields. The placement and design of 101 additional sensors allow resolution of toroidal mode numbers 1 ≤ n ≤ 3, and poloidal wavelengths smaller than MARS-F, IPEC, and VMEC magnetohydrodynamic model predictions. Small 3D perturbations, relative to the equilibrium field (10(-5)δB/B010(-4)), require sub-millimeter fabrication and installation tolerances. This high precision is achieved using electrical discharge machined components, and alignment techniques employing rotary laser levels and a coordinate measurement machine. A 16-bit data acquisition system is used in conjunction with analog signal-processing to recover non-axisymmetric perturbations. Co-located radial and poloidal field measurements allow up to 14.2 cm spatial resolution of poloidal structures (plasma poloidal circumference is ~500 cm). The function of the new system is verified by comparing the rotating tearing mode structure, measured by 14 BP fluctuation sensors, with that measured by the upgraded B(R) saddle loop sensors after the mode locks to the vessel wall. The result is a nearly identical 2/1 helical eigenstructure in both cases.

Experimental tests of ion poloidal rotation theories have been performed on DIII-D using a novel impurity poloidal rotation diagnostic. These tests show significant disagreements with theoretical predictions in various conditions, including L-mode plasmas with internal transport barriers (ITB), H-mode plasmas, and QH-mode plasmas. The theories tested include standard neoclassical theory, turbulence driven Reynolds stress, and fast-ion friction on the thermal ions. Poloidal rotation is observed to spin up at the formation of an ITB and makes a significant contribution to the measurement of the E→×B→ shear that forms the ITB. In ITB cases, neoclassical theory agrees quantitatively with the experimental measurements only in the steep gradient region. Significant quantitative disagreement with neoclassical predictions is seen in the cores of ITB, QH-, and H-mode plasmas, demonstrating that neoclassical theory is an incomplete description of poloidal rotation. The addition of turbulence driven Reynolds stress ...

A new transport model that uses neural networks (NNs) to yield electron and ion heat flux profiles has been developed. Given a set of local dimensionless plasma parameters similar to the ones that the highest fidelity models use, the NN model is able to efficiently and accurately predict the ion and electron heat transport profiles. As a benchmark, a NN was built, trained, and tested on data from the 2012 and 2013 DIII-D experimental campaigns. It is found that NN can capture the experimental behavior over the majority of the plasma radius and across a broad range of plasma regimes. Although each radial location is calculated independently from the others, the heat flux profiles are smooth, suggesting that the solution found by the NN is a smooth function of the local input parameters. This result supports the evidence of a well-defined, non-stochastic relationship between the input parameters and the experimentally measured transport fluxes. The numerical efficiency of this method, requiring only a few CPU-μs per data point, makes it ideal for scenario development simulations and real-time plasma control.

Physics based integrated modelling of the baseline scenario for a Fusion Nuclear Science Facility based on the Advanced Tokamak concept (FNSF-AT) (Chan et al 2010 Fusion Sci. Technol. 57 66) has found steady-state equilibria with good stability and controllability properties at the fusion performance required to accomplish FNSF's nuclear science mission with margin. 2D divertor analysis for this baseline scenario predicts that peak heat flux 1. Two current drive scenarios, two divertor configurations, and two blanket concepts have been analysed. FNSF-AT would complement ITER in addressing science and technology gaps to a commercially attractive DEMO, and could enable a DEMO construction decision triggered by the achievement of Q = 10 in ITER.

The Trapped Gyro-Landau Fluid (TGLF) quasi-linear model [G. M. Staebler, et al., Phys. Plasmas 12, 102508 (2005)], which is calibrated to nonlinear gyrokinetic turbulence simulations, is now able to predict the electron density, electron and ion temperatures, and ion toroidal rotation simultaneously for internal transport barrier (ITB) discharges. This is a strong validation of gyrokinetic theory of ITBs, requiring multiple instabilities responsible for transport in different channels at different scales. The mystery of transport inside the ITB is that momentum and particle transport is far above the predicted neoclassical levels in apparent contradiction with the expectation from the theory of suppression of turbulence by E×B velocity shear. The success of TGLF in predicting ITB transport is due to the inclusion of ion gyro-radius scale modes that become dominant at high E×B velocity shear and to improvements to TGLF that allow momentum transport from gyrokinetic turbulence to be faithfully modeled.

Ideal MHD stability limits of anticipated plasma configurations for the National Spherical Torus Experiment (NSTX) [Ono, M., et al., Nucl. Fusion 40 (2000) 557] and the dependence on the parameters defining the MHD equilibrium are evaluated. The study provides a quantitative computational evaluation of the stability limit variations induced by changes to the equilibrium of NSTX high-beta plasmas. The analysis is based on a reference free-boundary equilibrium with beta = 41.5%, monotonic safety factor q profile, and broad pressure profile p. On this reference target local variation of the plasma boundary, safety factor q, and pressure p profiles are imposed. Localized inflection of the outboard plasma boundary, produced by near-field effects from poloidal shaping field coils, weaken the stability due to the destabilization of high-n ballooning modes. Variation of the q profile at different radial location can also degrade stability. Both experimental profiles from existing tokamaks and spherical torus machines and profiles generated from transport modeling of anticipated neutral-beam-heated plasmas are used. Degraded stability is found at increasing pressure peaking factor due to the destabilization of n = 1 kink/ballooning modes. Direct access to the second region of stability is found in certain configurations and, for the entire set of variations considered, the lower calculated beta-limits values are still in the range of 20.0% without considering the stabilizing effect of the passive conducting structures.

A local representation is used to determine localized features in the current profiles due to ECCD in the DIII-D tokamak discharges from equilibrium reconstruction based on spectroscopic and external magnetic measurements. Initial results indicate that reconstruction using a local basis function can resolve very peaked ECCD profiles. The reconstructed narrow ECCD profiles are consistent with the quasi-linear Fokker-Planck results from the CQL3D code.

A variational ideal magnetohydrodynamic stability code is used to compute the toroidicity‐induced Alfven eigenmode (TAE) for toroidal mode number n=1 in full toroidal geometry with circular cross section. At finite aspect ratio, toroidicity also couples poloidal mode numbers m with m+2 to produce a higher frequency gap in the shear Alfven spectrum, which is associated with a new, second‐order TAE mode. It is also found that toroidal coupling between the TAE modes and continuum branches induces splitting of the TAE modes into two or more global modes at slightly different frequencies. Both the new modes and splitting of the TAE modes have important consequences for the identification of TAE modes in experiments.

Plasma equilibrium is an important basis for tokamak plasma research. The equilibrium reconstructed from experimental diagnostics is a key element for experiments analysis and for theory study. The kinetic equilibrium has the profiles information (current or safety factor profile, kinetic pressure profile), which are key issues for some studies of physics. With the constraints of magnetic measurements, pressure profile and edge current profile, we achieved the first reconstructed kinetic equilibrium on EAST tokamak. The pressure and edge current profiles are based on the diagnostics and theoretical bootstrap current model. The kinetic equilibrium has the pedestal structure for H-mode plasma, which the magnetic reconstruction missed. This improved equilibrium is an important basis for some experimental analysis and theory studies on EAST.

Advanced tokamaks seek to achieve a high bootstrap current fraction without sacrificing fusion power density or fusion gain. Good progress has been made towards the DIII-D research goal of demonstrating a high-β advanced tokamak plasma in steady state with a relaxed, fully non-inductive current profile and a bootstrap current fraction greater than 50%. The limiting factors for transport, stability, and current profile control in advanced operating modes are discussed in this paper.

During 1998, the General Atomics (GA) ARIES-Spherical Torus (ST) team examined several critical issues related to the physics performance of the ARIES-ST design, and a number of suggestions were made concerning possible improvements in performance. These included specification of a reference plasma equilibrium, optimization about the reference equilibrium to achieve higher beta limits, examination of three possible schemes for plasma initiation, development of a detailed scenario for ramp-up of the plasma current and pressure to its full, final operating values, an assessment of the requirement for electron confinement, and several suggestions for divertor heat flux reduction. The reference equilibrium was generated using the TOQ code, with the specification of a 100%, self-consistent bootstrap current. The equilibrium has {beta} = 51%, 10% below the stability limit (a margin specified by the ARIES-ST study). In addition, a series of intermediate equilibria were defined, corresponding to the ramp-up scenario discussed. A study of the influence of shaping on ARIES-ST performance indicates that significant improvement in both kink and ballooning stability can be obtained by modest changes in the squareness of the plasma. In test equilibria the ballooning beta limit is increased from 58% to 67%. Also the maximum allowable plasma-wall separation for kink stability can be increased by 30%. Three schemes were examined for noninductive plasma initiation. These are helicity injection (HICD), electron cyclotron heating (ECH)-assisted startup, and inductive startup using only the external equilibrium coils. HICD startup experiments have been done on the HIT and CDX devices. ECH-assisted startup has been demonstrated on CDX-U and DIII-D. External coil initiation is based on calculations for a proposed DIII-D experiment. In all cases, plasma initiation and preparation of an approximately 0.3 MA plasma for ARIES-ST appears entirely feasible.

Linear, two-fluid, resistive modelling of the plasma response to applied non-axisymmetric fields shows significant displacement of edge temperature and density profiles. The calculated displacements, often of 2 cm or more in H-mode pedestals with parameters appropriate to DIII-D, are due to the helical distortions resulting from stable edge modes being driven to finite amplitude by the applied fields. In many cases, these displacements are greater in magnitude, and different in phase, than the distortions of the separatrix manifolds predicted from vacuum modelling. Comparison of these results with experimental measurements from Thomson scattering and soft x-ray imaging finds good quantitative agreement. In these experiments, the phase of the applied non-axisymmetric magnetic field was flipped or rotated in order to probe the non-axisymmetric features of the response. The poloidal structures measured by x-ray imaging show clear indications of a helical response, as opposed to simply a change in the axisymmetric transport. Inclusion of two-fluid effects and rotation are found to be important in obtaining quantitative agreement with Thomson scattering data. Modelling shows screening of islands in the H-mode pedestal, but island penetration near the top of the pedestal where the electron rotation vanishes in plasmas with co-current rotation. Enhanced transport due to these islands may provide a mechanism for maintaining the pedestal width below the stability threshold of edge-localized modes. For typical DIII-D parameters, it is shown that the linear approximation is often near or beyond the limit of validity in the H-mode edge; however, the general agreement with experimental measurements indicates that these linear results nevertheless maintain good predictive value for profile displacements.

With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10 3 relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.

Author(s): Lazarus, EA; Navratil, GA; Greenfield, CM; Strait, EJ; Austin, ME; Burrell, KH; Casper, TA; Baker, DR; DeBoo, JC; Doyle, EJ; Durst, R; Ferron, JR; Forest, CB; Gohil, P; Groebner, RJ; Heidbrink, WW; Hong, R; Houlberg, WA; Howald, AW; Hsieh, C; Hyatt, AW; Jackson, GL; Kim, J; Lao, LL; Lasnier, CJ; Leonard, AW; Lohr, J; La Haye RJ; Maingi, R; Miller, RL; Murakami, M; Osborne, TH; Perkins, LJ; Petty, CC; Rettig, CL; Rhodes, TL; Rice, BW; Sabbagh, SA; Schissel, DP; Scoville, JT; Snider, RT; Staebler, GM; Stallard, BW; Stambaugh, RD; St John HE; Stockdale, RE; Taylor, PL; Thomas, DM; Turnbull, AD; Wade, MR; Wood, R; Whyte, D | Abstract: Fusion power has been increased by a factor of 3 in DIII-D by tailoring the pressure profile to avoid the kink instability in H-mode plasmas. The resulting plasmas are found to have neoclassical ion confinement. This reduction in transport losses in beam-heated plasmas with negative central shear is correlated with a dramatic reduction in density fluctuations. Improved magnetohydrodynamic stability is achieved by controlling the plasma pressure profile width. In deuterium plasmas the highest gain Q (the ratio of fusion power to input power), was 0.0015, corresponding to an equivalent Q of 0.32 in a deuterium-tritium plasma. © 1996 The American Physical Society.

The noninductive part of the measured current profile has been determined for DIII-D plasmas. A technique for determining the flux surface average of the quantity $\mathbf{E}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{B}$ and a model for the resistivity separates the current profile into inductive and noninductive portions. Analysis shows directly that neoclassical resistivity is adequate to explain the experimental observations, while Spitzer resistivity is not, and that a large noninductive current exists in plasmas for which large neutral beam current drive and pressure driven bootstrap currents are expected.

The extension of the EFIT equilibrium reconstruction code to fine spatial-grid resolutions is discussed. The residue in the force-balance relation of the Grad?Shafranov (G?S) equation and the convergence property of these fine spatial-grid EFIT equilibria are studied in detail. The results suggest that fine spatial-grid equilibria generally better satisfy the force-balance constraint described by the G?S equation. Finer spatial-grid equilibria have typically smaller average error in satisfying the force-balance equation than coarse-grid equilibria and those extrapolated from coarse-grid results. Analysis of the equilibrium iteration algorithm employed in EFIT reveals that the iteration process is related to the spatial feedback stabilization of the plasma with flux control at various specified locations. Thus, for a converged equilibrium, axisymmetric stability is generally expected with feedback. The iteration error decreases self-similarly in the final stage of the iteration process and is related to the least stable axisymmetric mode in the feedback-stabilized equilibrium.

Motivated by the recent experimental observation that plasma stability can be improved by external magnetic perturbations, the general problem of plasma response to external magnetic perturbations is investigated. Different (vacuum, ideal and resistive) plasma response models are considered and compared. Plasma response, in experiments where stabilization was achieved, is obtained through computation using the MARS-F code, with a plasma model that includes both plasma resistivity and rotation. The resultant magnetic field line stochasticity is much reduced from that obtained formerly using the vacuum plasma model. This reduced stochasticity is more consistent with the favourable experimental observation of enhanced stability. Examples are given for the response of an ITER plasma to perturbations generated by the correction coils; and the response of a plasma to external coils (antenna) up to the Alfvén frequency.

MHD simulations of rapid shutdown scenarios by massive particle injection in DIII-D, Alcator C-Mod and ITER are performed in order to study runaway electron (RE) transport during mitigated disruptions. The simulations include a RE confinement model using drift-orbit calculations for test particles. A comparison of limited and diverted plasma shapes is studied in DIII-D simulations, and improved confinement in the limited shape is found due to both spatial localization and reduced toroidal spectrum in the nonlinear MHD activity. C-Mod simulations compare shutdown scenarios in which impurity (Ar) fuelling is concentrated in the edge versus the core, and the confinement of REs in the core is maintained until the onset of the m = 1/n = 1 mode, which is delayed in the case of edge deposition, relative to core deposition. But, the overall RE loss fraction is 100% regardless of Ar fuelling profile. A comparison of simulations across the three devices points to a trend of increased RE confinement with increasing device size, wherein all REs are lost in C-Mod, all are confined in ITER, and a partial loss is observed in DIII-D. This trend is related to a reduction in the fluctuating field amplitude near the plasma edge during the thermal-quench-induced MHD activity. The result bodes poorly for RE mitigation strategies in ITER that rely on MHD deconfinement of REs.

The five-dimensional finite-orbit Monte Carlo code ORBIT-RF [M. Choi et al., Phys. Plasmas 12, 1 (2005)] is successfully coupled with the two-dimensional full-wave code all-orders spectral algorithm (AORSA) [E. F. Jaeger et al., Phys. Plasmas 13, 056101 (2006)] in a self-consistent way to achieve improved predictive modeling for ion cyclotron resonance frequency (ICRF) wave heating experiments in present fusion devices and future ITER [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)]. The ORBIT-RF/AORSA simulations reproduce fast-ion spectra and spatial profiles qualitatively consistent with fast ion D-alpha [W. W. Heidbrink et al., Plasma Phys. Controlled Fusion 49, 1457 (2007)] spectroscopic data in both DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 41, 1435 (2001)] high harmonic ICRF heating experiments. This work verifies that both finite-orbit width effect of fast-ion due to its drift motion along the torus and iterations between fast-ion distribution and wave fields are important in modeling ICRF heating experiments.

The tokamak plasmas in most of the present experiments and those considered for the future reactors are up–down asymmetric in nature. This asymmetry arises due to external coils and conducting structures which surround the plasma. The analytical description of these equilibria using mathematically simpler methods is useful for the theoretical study of stability and transport. Such a tokamak equilibrium has been constructed analytically for arbitrary aspect ratios. The asymmetric nature arises through the homogeneous part of the exact solution of the Grad–Shafranov equation with a choice of pressure and toroidal function as linear in poloidal flux. These solutions can describe both single- and double-null divertor plasmas with an appropriate choice of plasma boundary. This has been used to construct DIII-D and ITER-like equilibrium and compared with those computed numerically.

The Korea Superconducting Tokamak Advanced Research, KSTAR, is designed to operate a steady-state, high beta plasma while retaining global magnetohydrodynamic (MHD) stability to establish the scientific and technological basis of an economically attractive fusion reactor. An equilibrium model is established for stability analysis of KSTAR. Reconstructions were performed for the experimental start-up scenario and experimental first plasma operation using the EFIT code. The VALEN code was used to determine the vacuum vessel current distribution. Theoretical high beta equilibria spanning the expected operational range are computed for various profiles including generic L-mode and DIII-D experimental H-mode pressure profiles. Ideal MHD stability calculations of toroidal mode number of unity using the DCON code shows a factor of 2 improvement in the wall-stabilized plasma beta limit at moderate to low plasma internal inductance. The planned stabilization system in KSTAR comprises passive stabilizing plates and actively cooled in-vessel control coils (IVCCs) designed for non-axisymmetric field error correction and stabilization of slow timescale MHD modes including resistive wall modes (RWMs). VALEN analysis using standard proportional gain shows that active stabilization near the ideal wall limit can be reached with feedback using the midplane segment of the IVCC. The RMS power required for control using both white noise and noise taken from NSTX active stabilization experiments is computed for beta near the ideal wall limit. Advanced state-space control algorithms yield a factor of 2 power reduction assuming white noise while remaining robust with respect to variations in plasma beta.

Fast shutdowns of DIII-D and ITER plasmas are simulated in 3D with the NIMROD code. The simulations assume uniform deposition of deuterium, raising the total electron density by factors of 100–150. Under these conditions, the plasma is found to be stable to n = 1 and n = 2 instabilities for the duration of the shutdown. However, 2D effects are significant, particularly in the evolution of the electron density, which tends to drop as recombination occurs in the cold edge plasma. The DIII-D simulation finds that a factor of 100 densification will not enable collisional suppression of runaway electron avalanching. Although the ITER simulation marginally exceeds the threshold for avalanche suppression, ITER is a more promising candidate to remain in the avalanche-free regime given carefully tailored initial conditions.

Disruption mitigation experiments using massive gas injection (MGI) on Alcator C-Mod [Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] and DIII-D [Luxon and Davis, Fusion Technol. 8, 441 (1985)] have shown that magnetohydrodynamics (MHD) plays an important role. The three-dimensional MHD code NIMROD [Sovinec et al., J. Comput. Phys. 195, 355 (2004)] has been extended to include atomic physics taken from the KPRAD code to perform simulations of MGI. Considerable benchmarking of the code has been done against Alcator C-Mod for neon and helium gas jet experiments. The code successfully captures the qualitative sequence of events observed in MGI experiments up to the end of the thermal quench. Neon jet simulations also show quantitative agreement with the experimental thermal quench onset time. For helium gas jets, we show that a small percent boron density can significantly alter the results even in the presence of a helium jet with three orders of magnitude higher density. The thermal quench onset time is c...

The ideal MHD stability for double transport barrier (DTB or DB) plasmas with varying edge and internal barrier width and height was investigated, using the ideal MHD stability code GATO. A moderate ratio of edge transport barriers (ETB) height to internal transport barriers (ITBs) height is found to be beneficial to MHD stability and the ?N is limited by global low n instabilities. For moderate ITB width DB plasmas, if the ETB is weak, the stability is limited by n = 1 (n is the toroidal mode number) global mode; whereas if the ETB is strong it is limited by intermediate-n edge peeling?ballooning modes. Broadening the ITB can improve stability if the ITB half width wi 0.3. For very broad ITB width plasmas the stability is limited by stability to a low n (n > 1) global mode.

Plasmas with zero or near-zero current density in a wide region of the core have been produced in DIII-D discharges. The discharges were obtained with early neutral beam and electron cyclotron heating (ECH) during the plasma current ramp. Wide current holes (CHs) with a near-zero field over about 23% of the plasma width and narrow CHs with a duration of up to 1.1 s (comparable to the current relaxation time) have been obtained. Equilibria and pressure profiles were obtained by including kinetic and motional Stark effect (MSE) data using the code TRANSP. Agreement between calculated and measured neutron fluxes is obtained only when the fast-ion diffusion coefficient is set to very high values which results in considerable fast-ion redistribution and a broadened pressure profile. The MSE-only equilibrium fits are in good agreement with such kinetic fits. While CHs collapse due to tearing modes, bursty MHD activity coherent with electron temperature relaxation events is observed when the CHs are sustained. Some collapse events also appear to be coincident with edge localized modes. The CH phase seems to have been limited by the no-wall beta limit. In the present set of discharges, wider CHs (steeper temperature gradients) appear to collapse at somewhat lower β. Tearing modes are seen to cause shrinking of the CH. While early electron heating is strongly dependent on the timing and power of the neutral beam and by the ECH power, it is seen that larger neutral beam powers are correlated with wider CHs which do not decay significantly. An extensive and perhaps difficult analysis of current transport is required to check whether a neoclassical poloidal flux evolution (diffusive EMF) is either consistent with a stationary current profile or that an additional or anomalous EMF is present.

Recent results from the DIII-D tokamak have provided significant contributions to the understanding of many of the elements of tokamak physics and the application of this understanding to the design of next generation devices including ITER and CIT. The limitations of magnetohydrodynamic stability on the values of plasma beta (the ratio of kinetic pressure to the containing pressure of the magnetic field) that can be attained has been experimentally demonstrated and found to be described by existing theory. Values of beta (10.7%) well in excess of those required for proposed devices (ITER and CIT) have been demonstrated. Regimes of confinement (H-mode) have been established that scale favorably to proposed next generation devices, and experiments demonstrating the dependence of the energy confinement on plasma size have been completed. Understanding of confinement is rapidly developing especially in the areas of bulk transport and the role of turbulence in the plasma edge. Key experimental results in areas of plasma transport and edge plasma phenomena are in agreement with theories based on short wavelength turbulence. Control of the divertor heat loads and impurity influx has been demonstrated, and new progress has been made in the understanding of plasma edge phenomena. Experiments with ion Bernstein wave heating have not found regimes in which these waves can produce effective central ion heating. Electron cyclotron current drive experiments have demonstrated 70 kA of driven current in 400 kA discharges.

The stability of resistive modes is examined using reconstructions of experimental equilibria in the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)], revealing the important physics in mode onset as discharges evolve to instability. Experimental attempts to access the highest β in tokamak discharges, including “hybrid” discharges, are typically terminated by the growth of a large 2∕1 tearing mode. Model equilibria, based on experimental reconstructions from one of these discharges with steady state axial q0≈1, are generated varying q0 and pressure. For each equilibrium, the PEST-III code [A. Pletzer, A. Bondeson, and R. L. Dewar, J. Comput. Phys. 115, 530 (1994)] is used to determine the ideal magnetohydrodynamic solution including both tearing and interchange parities. This outer region solution must be matched to the resistive inner layer solutions at the rational surface to determine resistive mode stability. From this analysis it is found that the approach to q=1 simultaneo...

The role of interchange and internal kink modes in the sawtooth oscillations is explored by comparing bean- and oval-shaped plasmas. The n=1 instability that results in the collapse of the sawtooth has been identified as a quasi-interchange in the oval cases and the internal kink in the bean shape. The ion and electron temperature profiles are followed in detail through the sawtooth ramp. It is found that electron energy transport rates are very high in the oval and quite low in the bean shape. Ion energy confinement in the oval is excellent and the sawtooth amplitude (δT∕T) in the ion temperature is much larger than that of the electrons. The sawtooth amplitudes for ions and electrons are comparable in the bean shape. The measured q profiles in the bean and oval shapes are found to be consistent with neoclassical current diffusion of the toroidal current, and the observed differences in q largely result from the severe differences in electron energy transport. For both shapes the collapse flattens the q ...

The possibility of kinetic Alfven wave current drive at the center of tokamaks is proposed. The amount of driven current could be substantial and strongly affect the dynamics of the plasma central region. The relevance of this mechanism to present day and future tokamaks operating in the hybrid regime is discussed.

Recent QH-mode research on DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] has used the peeling-ballooning modes model of edge magnetohydrodynamic stability as a working hypothesis to organize the data; several predictions of this theory are consistent with the experimental results. Current ramping results indicate that QH modes operate near the edge current limit set by peeling modes. This operating point explains why QH mode is easier to get at lower plasma currents. Power scans have shown a saturation of edge pressure with increasing power input. This allows QH-mode plasmas to remain stable to edge localized modes (ELMs) to the highest powers used in DIII-D. At present, the mechanism for this saturation is unknown; if the edge harmonic oscillation (EHO) is playing a role here, the physics is not a simple amplitude dependence. The increase in edge stability with plasma triangularity predicted by th...

The present performance limits of tokamak discharges are strongly coupled to the stability and transport properties of the edge plasma. Both experimental and modeling efforts have shown a clear connection between the edge pressure pedestal height and core plasma confinement. The key to understanding the stability and performance limits of the pedestal revolves around an accurate knowledge of the plasma current in this region. Using the Zeeman effect in an injected 30keV lithium beam, we have measured the currents in the edge of the DIII-D [J. L. Luxon, Nucl. Fusion 42, 6114 (2002)] tokamak for various confinement modes. This method of determining j(r) is insensitive to the large electric fields which coexist in the pedestal region and which complicate motional Stark effect measurements. For the high confinement cases, where substantial pedestal pressures exist, we find large (~MA∕m2), localized (ΔR∼1–2cm) currents in the pedestal region, located near the maximum in the pressure gradient. These values are ...

Motional Stark effect produces large net linear polarization of Hα emission from neutral beams in tokamaks. Measurement of the polarization direction permits determination of the local magnetic field pitch angle. Design of a single point, spatially scannable, high‐sensitivity polarimeter installed on DIII‐D is described. Excellent signal‐to‐noise ratio with good temporal and spatial resolution was obtained in preliminary measurements of magnetic field pitch angle.

Time resolved power deposition profiles on the D III-D divertor target plates have been measured for Ohmic and neutral beam injection heated plasmas using fast response infrared thermography (τ ≤ 150 μs). Giant Edge Localized Modes have been observed which punctuate quiescent periods of good H-mode confinement and deposit more than 5% of the stored energy of the core plasma on the divertor armour tiles on millisecond timescales. The heat pulse associated with these events arrives approximately 0.5 ms earlier on the outer leg of the divertor relative to the inner leg. The measured power deposition profiles are displaced relative to the separatrix intercepts on the target plates, and the peak heat fluxes are a function of core plasma density.

The ideal localized ballooning mode stability criterion has been analysed using equilibria obtained in Doublet III. Near the experimental beta limit, portions of the flux surfaces could have developed the pressure gradient set by this stability criterion. At low q (≤3.2), this is not sufficient to affect the trend in the development of the plasma internal inductance, , and total βt. At high q (≥3.5), both and βt achieve stationary values. This correlates well with the hypothesis that a large portion of the plasma reaches the ballooning mode limit for more than one energy confinement time.